Anonymous

Let Ө = x cos²Ө /sin²Ө x 1/cosӨ -------------------------------- cos²Ө x sin²Ө 1/cosӨ ---------------= sec Ө csc^4 Ө sin^4 Ө

Anonymous

cot^2x secx/(cos^2x sin^2x) = cos^2x/sin^2x * secx/(cos^2x sin^2x) = secx/sin^4x = secx csc^4x

Anonymous

cot^2(x)sec(x) / cos^2(x)sin^2(x) (left) = (cos^2(x) / sin^2(x)cos(x)) / cos^2(x)sin^2(x) = (cos(x) / sin^2(x)) / cos^2(x)sin^2(x) = cos(x) / cos^2(x)(sin^2(x))^2 = 1 / cos(x)sin^4(x) = (1/cos(x))(1/sin^4(x)) = sec(x)csc^4(x) (right). Done.

Anonymous

(cot^2 (x) × sec (x)) / (cos^2 (x) × sin^2 (x)) = csc^4 (x) × sec (x) = sec (x) × cosec^ 4 (x)

Anonymous

Identities cotx =cosx/sinx sec x = 1/cosx cosec x = 1/sinx

Anonymous

[cos^2(x)/sin^2(x) * 1/cosx]* 1/cos^2(x)*1/sin^2(x) = 1/sin^2(x) * 1/cosx]* 1/sin^2(x) = secx * 1/sin^4(x) = secx * csc^4(x)